1. Introduction to bioinformatics 2007 Lecture 11G A V B M S U
Introduction to bioinformatics 2007 Lecture 11
Multiple Sequence Alignment (III) and Evolution/Phylogenetic methods

2. Evaluating multiple alignments
There are reference databases based on structural information: e.g. BAliBASE and HOMSTRAD
Conflicting standards of truth
evolution
structure
function
With orphan sequences no additional information
Benchmarks depending on reference alignments
Quality issue of available reference alignment databases
Different ways to quantify agreement with reference alignment (sum-of-pairs, column score)
“Charlie Chaplin” problem

3. Evaluating multiple alignments
As a standard of truth, often a reference alignment based on structural superpositioning is taken
These superpositionings can be scored using the root-mean-square-deviation (RMSD) of atoms that are equivalenced (taken as corresponding) in a pair of protein structures

4. BAliBASE benchmark alignments
Thompson et al. (1999) NAR 27, 2682.
8 categories:
cat. 1 - equidistant
cat. 2 - orphan sequence
cat distant groups
cat. 4 – long overhangs
cat. 5 - long insertions/deletions
cat. 6 – repeats
cat. 7 – transmembrane proteins
cat. 8 – circular permutations

5. BAliBASE BB11001 1aab_ref1 Ref1 V1 SHORT high mobility group protein
BB aboA_ref1 Ref1 V1 SHORT SH3
BB ad3_ref1 Ref1 V1 LONG aldehyde dehydrogenase
BB adj_ref1 Ref1 V1 LONG histidyl-trna synthetase
BB ajsA_ref1 Ref1 V1 LONG aminotransferase
BB bbt3_ref1 Ref1 V1 MEDIUM foot-and-mouth disease virus BB cpt_ref1 Ref1 V1 LONG cytochrome p450
BB csy_ref1 Ref1 V1 SHORT SH2
BB dox_ref1 Ref1 V1 SHORT ferredoxin [2fe-2s] .

6. T-Coffee: correctly aligned Kinase nucleotide binding sites

7. Scoring a single MSA with the Sum-of-pairs (SP) score
Good alignments should have a high SP score, but it is not always the case that the true biological alignment has the highest score.
Sum-of-Pairs score
Calculate the sum of all pairwise alignment scores
This is equivalent to taking the sum of all matched a.a. pairs
The latter can be done using gap penalties or not

8. Evaluation measures Column score Sum-of-Pairs score Query Reference
What fraction of the MSA columns in the reference alignment is reproduced by the computed alignment
Sum-of-Pairs score
What fraction of the matched amino acid pairs in the reference alignment is reproduced by the computed alignment

9. Evaluating multiple alignments

10. Evaluating multiple alignments Charlie Chaplin problem
SP
BAliBASE alignment nseq * len

11. Evaluating multiple alignments Charlie Chaplin problem

12. Comparing T-coffee with other methods

13. BAliBASE benchmark alignments

14. Summary Individual alignments can be scored with the SP score.
Better alignments should have better SP scores
However, there is the Charlie Chaplin problem
A test and a reference multiple alignment can be scored using the SP score or the column score (now for pairs of alignments)
Evaluations show that there is no MSA method that always wins over others in terms of alignment quality

15. Lecture 11: Evolution/Phylogeny methods
Introduction to Bioinformatics

16. Bioinformatics
“Nothing in Biology makes sense except in the light of evolution” (Theodosius Dobzhansky ( ))
“Nothing in bioinformatics makes sense except in the light of Biology”

17. Evolution Most of bioinformatics is comparative biology
Comparative biology is based upon evolutionary relationships between compared entities
Evolutionary relationships are normally depicted in a phylogenetic tree

18. Where can phylogeny be used
For example, finding out about orthology versus paralogy
Predicting secondary structure of RNA
Studying host-parasite relationships
Mapping cell-bound receptors onto their binding ligands
Multiple sequence alignment (e.g. Clustal)

19. DNA evolution
Gene nucleotide substitutions can be synonymous (i.e. not changing the encoded amino acid) or nonsynonymous (i.e. changing the a.a.).
Rates of evolution vary tremendously among protein-coding genes. Molecular evolutionary studies have revealed an ∼1000-fold range of nonsynonymous substitution rates (Li and Graur 1991).
The strength of negative (purifying) selection is thought to be the most important factor in determining the rate of evolution for the protein-coding regions of a gene (Kimura 1983; Ohta 1992; Li 1997).

20. DNA evolution
“Essential” and “nonessential” are classic molecular genetic designations relating to organismal fitness.
A gene is considered to be essential if a knock-out results in (conditional) lethality or infertility.
Nonessential genes are those for which knock-outs yield viable and fertile individuals.
Given the role of purifying selection in determining evolutionary rates, the greater levels of purifying selection on essential genes leads to a lower rate of evolution relative to that of nonessential genes.

21. Reminder -- Orthology/paralogy
Orthologous genes are homologous (corresponding) genes in different species
Paralogous genes are homologous genes within the same species (genome)

22. Old Dogma – Recapitulation Theory (1866)
Ernst Haeckel:
“Ontogeny recapitulates phylogeny”
Ontogeny is the development of the embryo of a given species;
phylogeny is the evolutionary history of a species
Haeckels drawing in support of his theory: For example, the human embryo with gill slits in the neck was believed by Haeckel to not only signify a fishlike ancestor, but it represented a total fishlike stage in development. Gill slits are not the same as gills and are not functional.

23. Phylogenetic tree (unrooted)
human
Drosophila
internal node
fugu
mouse
leaf
OTU – Observed taxonomic unit
edge

24. Phylogenetic tree (unrooted)
human
Drosophila
internal node
fugu
mouse
leaf
OTU – Observed taxonomic unit
edge

25. Phylogenetic tree (rooted)
time
edge
internal node (ancestor)
leaf
OTU – Observed taxonomic unit
Drosophila
human
fugu
mouse

26. How to root a tree f m
Outgroup – place root between distant sequence and rest group
Midpoint – place root at midpoint of longest path (sum of branches between any two OTUs)
Gene duplication – place root between paralogous gene copies h D D f m h 1 f m 3 1 4 2 2 3 1 1 1 5 h D f m h D
f-
f-
h-
f-
h-
f-
h-
h-

27. Combinatoric explosion
Number of unrooted trees =
Number of rooted trees =

28. Combinatoric explosion
# sequences # unrooted # rooted
trees trees
,395
, ,135
,135 2,027,025
,027, ,459,425

29. Tree distances
Evolutionary (sequence distance) = sequence dissimilarity 5
human x
mouse x
fugu x
Drosophila x
human 1 2
mouse 1 1
fugu 6
Drosophila
human
mouse
fugu
Drosophila
Note that with evolutionary methods for generating trees you get distances between objects by walking from one to the other.

30. Phylogeny methods
Distance based – pairwise distances (input is distance matrix)
Parsimony – fewest number of evolutionary events (mutations) – relatively often fails to reconstruct correct phylogeny, but methods have improved recently
Maximum likelihood – L = Pr[Data|Tree] – most flexible class of methods - user-specified evolutionary methods can be used

31. Distance based --UPGMA
Let Ci and Cj be two disjoint clusters: 1
di,j = ———————— pq dp,q, where p  Ci and q  Cj
|Ci| × |Cj| Ci Cj
In words: calculate the average over all pairwise inter-cluster distances

32. Clustering algorithm: UPGMA
Initialisation:
Fill distance matrix with pairwise distances
Start with N clusters of 1 element each
Iteration:
Merge cluster Ci and Cj for which dij is minimal
Place internal node connecting Ci and Cj at height dij/2
Delete Ci and Cj (keep internal node)
Termination:
When two clusters i, j remain, place root of tree at height dij/2 d

33. Ultrametric Distances
A tree T in a metric space (M,d) where d is ultrametric has the following property: there is a way to place a root on T so that for all nodes in M, their distance to the root is the same. Such T is referred to as a uniform molecular clock tree.
(M,d) is ultrametric if for every set of three elements i,j,k∈M, two of the distances coincide and are greater than or equal to the third one (see next slide).
UPGMA is guaranteed to build correct tree if distances are ultrametric. But it fails if not!

34. Ultrametric Distances
Given three leaves, two distances are equal while a third is smaller:
d(i,j)  d(i,k) = d(j,k)
a+a  a+b = a+b i a
nodes i and j are at same evolutionary distance from k – dendrogram will therefore have ‘aligned’ leafs; i.e. they are all at same distance from root b k a j

35. Evolutionary clock speeds
Uniform clock: Ultrametric distances lead to identical distances from root to leafs
Non-uniform evolutionary clock: leaves have different distances to the root -- an important property is that of additive trees. These are trees where the distance between any pair of leaves is the sum of the lengths of edges connecting them. Such trees obey the so-called 4-point condition (next slide).

36. Additive trees All distances satisfy 4-point condition:
For all leaves i,j,k,l:
d(i,j) + d(k,l)  d(i,k) d(j,l) = d(i,l) d(j,k)
(a+b)+(c+d)  (a+m+c)+(b+m+d) = (a+m+d)+(b+m+c) k i a c m b j d l
Result: all pairwise distances obtained by traversing the tree

37. Additive trees
In additive trees, the distance between any pair of leaves is the sum of lengths of edges connecting them
Given a set of additive distances: a unique tree T can be constructed:
For two neighbouring leaves i,j with common parent k, place parent node k at a distance from any node m with
d(k,m) = ½ (d(i,m) + d(j,m) – d(i,j))
c = ½ ((a+c) + (b+c) – (a+b)) i a c m k b j
d is ultrametric ==> d additive

38. Distance based --Neighbour-Joining (Saitou and Nei, 1987)
Guaranteed to produce correct tree if distances are additive
May even produce good tree if distances are not additive
Global measure – keeps total branch length minimal
At each step, join two nodes such that the total tree length (sum of all branch lengths) is minimal (criterion of minimal evolution)
Agglomerative algorithm
Leads to unrooted tree

39. Neighbour joining y x x x y (c) (a) (b) x x x y y (f) (d) (e)
At each step all possible ‘neighbour joinings’ are checked and the one corresponding to the minimal total tree length (calculated by adding all branch lengths) is taken.

40. Algorithm: Neighbour joining
NJ algorithm in words:
Make star tree with ‘fake’ distances (we need these to be able to calculate total branch length)
Check all n(n-1)/2 possible pairs and join the pair that leads to smallest total branch length. You do this for each pair by calculating the real branch lengths from the pair to the common ancestor node (which is created here – ‘y’ in the preceding slide) and from the latter node to the tree
Select the pair that leads to the smallest total branch length (by adding up real and ‘fake’ distances). Record and then delete the pair and their two branches to the ancestral node, but keep the new ancestral node. The tree is now 1 one node smaller than before.
Go to 2, unless you are done and have a complete tree with all real branch lengths (recorded in preceding step)

41. Neighbour joining Finding neighbouring leaves: Define
Dij = dij – (ri + rj)
Where 1
ri = ——— k dik
|L| - 2
Total tree length Dij is minimal iff i and j are neighbours
Proof in Durbin book, p. 189

42. Algorithm: Neighbour joining
Initialisation:
Define T to be set of leaf nodes, one per sequence
Let L = T
Iteration:
Pick i,j (neighbours) such that Di,j is minimal (minimal total tree length)
Define new node k, and set dkm = ½ (dim + djm – dij) for all m  L
Add k to T, with edges of length dik = ½ (dij + ri – rj)
Remove i,j from L; Add k to L
Termination:
When L consists of two nodes i,j and the edge between them of length dij

43. Parsimony & Distance parsimony Sequences distance 1 2 3 4 5 6 7
Drosophila t t a t t a a
fugu a a t t t a a
mouse a a a a a t a
human a a a a a a t
Drosophila
mouse 1 6 4 5 2 3 7
human
fugu
distance
human x
mouse x
fugu x
Drosophila x
Drosophila 2
mouse 2 1 1 1
human
fugu
human
mouse
fugu
Drosophila

44. Problem: Long Branch Attraction (LBA)
Particular problem associated with parsimony methods
Rapidly evolving taxa are placed together in a tree regardless of their true position
Partly due to assumption in parsimony that all lineages evolve at the same rate
This means that also UPGMA suffers from LBA
Some evidence exists that also implicates NJ A A B D C B D
Inferred tree C
True tree

45. Maximum likelihood Pioneered by Joe Felsenstein
If data=alignment, hypothesis = tree, and under a given evolutionary model,
maximum likelihood selects the hypothesis (tree) that maximises the observed data
A statistical (Bayesian) way of looking at this is that the tree with the largest posterior probability is calculated based on the prior probabilities; i.e. the evolutionary model (or observations).
Extremely time consuming method
We also can test the relative fit to the tree of different models (Huelsenbeck & Rannala, 1997)

46. Maximum likelihood Methods to calculate ML tree:
Phylip (
Paup (
MrBayes (
Method to analyse phylogenetic tree with ML:
PAML (
The strength of PAML is its collection of sophisticated substitution models to analyse trees.
Programs such as PAML can test the relative fit to the tree of different models (Huelsenbeck & Rannala, 1997)

47. Maximum likelihood
A number of ML tree packages (e.g. Phylip, PAML) contain tree algorithms that include the assumption of a uniform molecular clock as well as algorithms that don’t
These can both be run on a given tree, after which the results can be used to estimate the probability of a uniform clock.

48. How to assess confidence in tree

49. How to assess confidence in tree
Distance method – bootstrap:
Select multiple alignment columns with replacement (scramble the MSA)
Recalculate tree
Compare branches with original (target) tree
Repeat times, so calculate different trees
How often is branching (point between 3 nodes) preserved for each internal node in these trees?
Bootstrapping uses resampling of the data

50. The Bootstrap -- example
Used multiple times in resampled (scrambled) MSA below
- C V K V I Y S
M A V R - I F S
M C L R L L F T
V K V S I I S I
V R V S I I S I
L R L T L L T L 5 1 2 3
Original 4 2x 3x 1 1 2 3
Non-supportive
Scrambled 5
Only boxed alignment columns are randomly selected in this example

51. Some versatile phylogeny software packages
MrBayes
Paup
Phylip

52. MrBayes: Bayesian Inference of Phylogeny
MrBayes is a program for the Bayesian estimation of phylogeny.
Bayesian inference of phylogeny is based upon a quantity called the posterior probability distribution of trees, which is the probability of a tree conditioned on the observations.
The conditioning is accomplished using Bayes's theorem. The posterior probability distribution of trees is impossible to calculate analytically; instead, MrBayes uses a simulation technique called Markov chain Monte Carlo (or MCMC) to approximate the posterior probabilities of trees.
The program takes as input a character matrix in a NEXUS file format. The output is several files with the parameters that were sampled by the MCMC algorithm. MrBayes can summarize the information in these files for the user.

53. MrBayes: Bayesian Inference of Phylogeny
MrBayes program features include:
A common command-line interface for Macintosh, Windows, and UNIX operating systems;
Extensive help available via the command line;
Ability to analyze nucleotide, amino acid, restriction site, and morphological data;
Mixing of data types, such as molecular and morphological characters, in a single analysis;
A general method for assigning parameters across data partitions;
An abundance of evolutionary models, including 4 X 4, doublet, and codon models for nucleotide data and many of the standard rate matrices for amino acid data;
Estimation of positively selected sites in a fully hierarchical Bayes framework;
The ability to spread jobs over a cluster of computers using MPI (for Macintosh and UNIX environments only).

54. PAUP

55. Phylip – by Joe Felsenstein
Phylip programs by type of data
DNA sequences
Protein sequences
Restriction sites
Distance matrices
Gene frequencies
Quantitative characters
Discrete characters
tree plotting, consensus trees, tree distances and tree manipulation

56. Phylip – by Joe Felsenstein
Phylip programs by type of algorithm
Heuristic tree search
Branch-and-bound tree search
Interactive tree manipulation
Plotting trees, consenus trees, tree distances
Converting data, making distances or bootstrap replicates

57. (B:6.0,(A:5.0,C:3.0,E:4.0):5.0,D:11.0); -- with branch lengths
The Newick tree format A C
Ancestor1 E 5 3 4 D B 11 6 5
(B,(A,C,E),D); -- tree topology
root
(B:6.0,(A:5.0,C:3.0,E:4.0):5.0,D:11.0); -- with branch lengths
(B:6.0,(A:5.0,C:3.0,E:4.0)Ancestor1:5.0,D:11.0)Root; -- with branch lengths and ancestral node names

58. Distance methods: fastest
Clustering criterion using a distance matrix
Distance matrix filled with alignment scores (sequence identity, alignment scores, E-values, etc.)
Cluster criterion

59. Phylogenetic tree by Distance methods (Clustering)1 2 3 4 5
Multiple
alignment
Similarity criterion
Similarity
matrix
Scores
5×5
Phylogenetic tree

60. Lactate dehydrogenase multiple alignment
Human KITVVGVGAVGMACAISILMKDLADELALVDVIEDKLKGEMMDLQHGSLFLRTPKIVSGKDYNVTANSKLVIITAGARQ
Chicken KISVVGVGAVGMACAISILMKDLADELTLVDVVEDKLKGEMMDLQHGSLFLKTPKITSGKDYSVTAHSKLVIVTAGARQ
Dogfish –KITVVGVGAVGMACAISILMKDLADEVALVDVMEDKLKGEMMDLQHGSLFLHTAKIVSGKDYSVSAGSKLVVITAGARQ
Lamprey SKVTIVGVGQVGMAAAISVLLRDLADELALVDVVEDRLKGEMMDLLHGSLFLKTAKIVADKDYSVTAGSRLVVVTAGARQ
Barley TKISVIGAGNVGMAIAQTILTQNLADEIALVDALPDKLRGEALDLQHAAAFLPRVRI-SGTDAAVTKNSDLVIVTAGARQ
Maizey casei -KVILVGDGAVGSSYAYAMVLQGIAQEIGIVDIFKDKTKGDAIDLSNALPFTSPKKIYSA-EYSDAKDADLVVITAGAPQ
Bacillus TKVSVIGAGNVGMAIAQTILTRDLADEIALVDAVPDKLRGEMLDLQHAAAFLPRTRLVSGTDMSVTRGSDLVIVTAGARQ
Lacto__ste -RVVVIGAGFVGASYVFALMNQGIADEIVLIDANESKAIGDAMDFNHGKVFAPKPVDIWHGDYDDCRDADLVVICAGANQ
Lacto_plant QKVVLVGDGAVGSSYAFAMAQQGIAEEFVIVDVVKDRTKGDALDLEDAQAFTAPKKIYSG-EYSDCKDADLVVITAGAPQ
Therma_mari MKIGIVGLGRVGSSTAFALLMKGFAREMVLIDVDKKRAEGDALDLIHGTPFTRRANIYAG-DYADLKGSDVVIVAAGVPQ
Bifido KLAVIGAGAVGSTLAFAAAQRGIAREIVLEDIAKERVEAEVLDMQHGSSFYPTVSIDGSDDPEICRDADMVVITAGPRQ
Thermus_aqua MKVGIVGSGFVGSATAYALVLQGVAREVVLVDLDRKLAQAHAEDILHATPFAHPVWVRSGW-YEDLEGARVVIVAAGVAQ
Mycoplasma -KIALIGAGNVGNSFLYAAMNQGLASEYGIIDINPDFADGNAFDFEDASASLPFPISVSRYEYKDLKDADFIVITAGRPQ
Distance Matrix
1 Human
2 Chicken
3 Dogfish
4 Lamprey
5 Barley
6 Maizey
7 Lacto_casei
8 Bacillus_stea
9 Lacto_plant
10 Therma_mari
11 Bifido
12 Thermus_aqua
13 Mycoplasma

61. Kimura’s correction for protein sequences (1983)
This method is used for proteins only. Gaps are ignored and only exact matches and mismatches contribute to the match score. Distances get ‘stretched’ to correct for back mutations
S = m/npos,
Where m is the number of exact matches and
npos the number of positions scored
D = 1-S
Corrected distance = -ln(1 - D - 0.2D2)
Reference: M. Kimura, The Neutral Theory of Molecular Evolution, Camb. Uni. Press, Camb., 1983.

62. Sequence similarity criteria for phylogeny
In addition to the Kimura correction, there are various models to correct for the fact that the true rate of evolution cannot be observed through nucleotide (or amino acid) exchange patterns (e.g. due to back mutations).
• Saturation level is ~94%, higher real mutations are no longer observable

63. A widely used protocol to infer a phylogenetic tree
Make an MSA
Take only gapless positions and calculate pairwise sequence distances using Kimura correction
Calculate a phylogenetic tree using Neigbour Joining (NJ)

64. How to assess confidence in tree
How sure are we about these splits?

65. How to assess confidence in tree The Bootstrap
Select multiple alignment columns with replacement
Recalculate tree using this fake alignment
Compare branches with original (target) tree
Repeat times, so calculate different trees
How often is branching (point between 3 nodes) preserved for each internal node?
Uses samples of the data

66. The Bootstrap 1 2 3 4 5 6 7 8 C C V K V I Y S M A V R L I F S
M C L R L L F T
V K V S I I S I
V R V S I I S I
L R L T L L T L 5 1 2 3
Original 4 2x 3x 1 1 2 3
Non-supportive
Scrambled 5

67. Phylogeny disclaimer
With all of the phylogenetic methods, you calculate one tree out of very many alternatives.
Only one tree can be correct and depict evolution accurately.
Incorrect trees will often lead to ‘more interesting’ phylogenies, e.g. the whale originated from the fruit fly etc.

68. Take home messages Orthology/paralogy Rooted/unrooted trees
Make sure you can do the UPGMA algorithm and understand the basic steps of the NJ algorithm
Understand the three basic classes of phylogenetic methods: distance, parsimony and maximum likelihood
Make sure you understand bootstrapping (to asses confidence in tree splits)